SIMULATION OF THE FORCE INTERACTION OF THE SOIL COMPACTING DISK MOVING ALONG A RHEOLOGICAL BEAM THAT HAS DISTRIBUTED MASS
Pages 60 - 64
The authors describe an original solution to the new problem of a soil compacting disk moving along a rheological beam (Kelvin model) in the proposed paper. The motion of the mechanical system that is composed of a disk and a rheological beam is described by a hybrid system of differential equations consisting of an integral-differential equation that stands for the interaction of the beam with a moving disk and Lagrange equations describing the pattern of the disk motion.
These equations are considered as equations of nonholonomic links. The problem is solved through the employment of simplifying prerequisites and by determining the operating condition of the disk.
Condition of uniform and uniformly variable motions is considered as an opportunity to integrate the equation of beam vibrations regardless of the system of equations describing the disk motion pattern. The solution to the equation in partial derivatives is found through the employment of the Fourier method of separation of variables coupled with the Laplace integral transformation method. The solution to the problem of constrained vibrations was implemented as a series of homogenous problems with zero initial and boundary conditions.
The equation describing changes in the time function is reduced to its standard form, and thereafter the solution is found through the employment of asymptotic methods. Disk motion stability is assessed through the employment of the first approximation method. The motion of the disk is stable. As a result of the analysis of patterns of dependencies between beam deformations and the time period, the conclusion of feasibility of a stable pattern of forced vibrations of a rheological beam, supported by a driving force and a variable friction force, caused by the slightly elastic field of the beam material, is made by the authors.
DOI: 10.22227/1997-0935.2012.7.60 - 64
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